Abstract
A Banach space operator $T$ satisfies property($Bgw$), a variant property$(gw)$, if the complement in the approximate point spectrum $\sigma_{a}(T)$ of the semi-B-essential approximate point spectrum $\sigma_{SBF^{-}_{+}}(T)$ coincides with set of isolated eigenvalues of $T$ of finite multiplicity $E^{0}(T)$. We also introduce properties $(Bb)$, and property $(Bgb)$ in connection with Weyl type theorems, which are analogous, respectively, to generalized Browder's theorem and property($gb$). We obtain relation among these new properties.
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